state and prove the pythogoras theoram give full explaination please from A to Z clear cut sol i want okk frnds please
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Here is ur answer......
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Given :-
A right angled triangle right angled at B.
To prove :-
AB²+BC²=AC²
construction :-
Draw AD perpendicular to AC.
Proof :-
In triangle ABC & ABD,
angle A =angle A (common)
Angle ADB =Angle ABC =90°(right angles)
Triangle ABC ~ABD by (AA similarity)
AD/AB =AB/AC..... By cpct
AB ² = AD×AC............... eq1
Now,
In triangle BDC&ABC,
Angle C = Angle C (common)
Angle BDC= Angle ABC (Right angled)
So triangle BDC~ABC (by AA similarity)
CD/BC=BC/AC.... by cpct
BC² = CD×AC............... eq2
Now by adding eq 1 & 2 we have,
AB²+BC²=AD×AC+CD×AC
AB²+BC²=AC(AD+CD)
AB²+BC²=AC×AC
AB²+BC²=AC²
Hence proved.
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